Subgroups — C₂×#20244096 #26219017

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689151	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689119	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689090	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244096	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688887	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#104×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	#15689151	—	2	2	no	—
14	#15689151	C₂²	1	4	yes	complemented
15	C₂×Dic₄₇⋊C₈	—	2	2	no	—
16	#15689119	C₄	1	4	yes	complemented
17	#15689119	C₂²	1	4	yes	—
18	C₂×#13093948	C₄	1	2	yes	complemented
19	C₂×#13093945	C₄	1	2	yes	complemented
20	#15689090	—	2	2	no	—
21	#15689090	C₂²	1	4	yes	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
23	C₂×#13093935	—	2	4	no	—
24	C₂×#13093935	C₂²	1	4	yes	complemented
25	#15688887	C₂²	1	4	yes	complemented
26	#15688883	C₂²	1	4	yes	complemented
27	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#104×C₄₇	—	2	4	no	—
31	C₂×#104×C₄₇	C₂²	1	4	yes	—
32	C₂×#10625329	—	2	1	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	C₂³	1	2	yes	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	C₂²×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
44	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	#13093983	—	2	1	no	—
48	#13093983	—	2	1	no	—
49	#13093983	C₂×C₄	1	2	yes	—
50	#13093983	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
53	C₂×C₄×Dic₄₇	—	2	1	no	—
54	Dic₄₇⋊C₈	—	2	8	no	—
55	#13093948	C₂×C₄	1	8	yes	complemented
56	#13093945	C₂×C₄	1	8	yes	complemented
57	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
58	#13093935	—	2	8	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	—	2	1	no	—
61	C₂×#41×C₄₇	—	2	2	no	—
62	C₂×#41×C₄₇	—	2	2	no	—
63	C₂×#41×C₄₇	—	2	2	no	—
64	C₂×#41×C₄₇	—	2	2	no	—
65	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×#41×C₄₇	C₂³	1	2	yes	—
67	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₄₇	—	2	1	no	—
69	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂³×C₄×C₄₇	—	2	1	no	—
72	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₇	—	2	1	no	—
74	C₂×M₁₆×C₄₇	—	2	2	no	—
75	C₂×M₁₆×C₄₇	—	2	2	no	—
76	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	D₄	1	4	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	#104×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	—	2	1	no	—
84	C₂⁴×C₄₇	#41	1	1	yes	characteristic
85	#41×C₄₇	—	2	4	no	—
86	#41×C₄₇	—	2	4	no	—
87	#41×C₄₇	—	2	2	no	—
88	#41×C₄₇	—	2	2	no	—
89	#41×C₄₇	—	2	2	no	—
90	#41×C₄₇	—	2	2	no	—
91	#41×C₄₇	—	4	2	no	—
92	#41×C₄₇	—	4	2	no	—
93	#41×C₄₇	—	4	2	no	—
94	#41×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	4	2	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	4	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	#41	1	2	yes	—
121	C₂²×C₄×C₄₇	#41	1	2	yes	—
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	—	2	2	no	—
126	M₁₆×C₄₇	—	2	2	no	—
127	M₁₆×C₄₇	—	2	2	no	—
128	M₁₆×C₄₇	—	4	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂×D₄	1	4	yes	—
134	C₂²⋊Dic₄₇	—	2	2	no	—
135	C₂²⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	#10625329	—	2	2	no	—
141	#10625329	—	2	2	no	—
142	#10625329	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	2	4	no	—
144	C₂×C₄₇⋊C₈	—	2	4	no	—
145	C₂×C₄₇⋊C₈	—	2	4	no	—
146	C₂×C₄₇⋊C₈	—	2	4	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	4	2	no	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
155	C₂³×C₄₇	—	2	4	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	4	no	—
159	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₇	#123	1	2	yes	—
162	C₂³×C₄₇	#126	1	2	yes	—
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	2	2	no	—
168	D₄×C₄₇	—	2	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	4	2	no	—
171	D₄×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	8	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	#117	1	2	yes	—
182	C₂×C₄×C₄₇	#117	1	2	yes	—
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₇	#121	1	2	yes	—
188	C₂×C₄×C₄₇	#121	1	2	yes	—
189	C₂×C₄×C₄₇	#123	1	2	yes	—
190	C₂×C₄×C₄₇	#124	1	2	yes	—
191	C₂×C₄×C₄₇	#124	1	2	yes	—
192	C₂×C₄×C₄₇	#126	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₄₇	—	2	4	no	—
200	C₂×Dic₄₇	—	4	4	no	—
201	C₈×C₄₇	—	4	2	no	—
202	C₄₇⋊C₈	—	2	4	no	—
203	C₄₇⋊C₈	—	2	4	no	—
204	C₄₇⋊C₈	—	4	2	no	—
205	C₂×#1938	—	47	1	no	maximal, Sylow
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	4	no	—
209	C₂²×C₄₇	—	2	4	no	—
210	C₂²×C₄₇	—	4	4	no	—
211	C₂²×C₄₇	—	4	2	no	—
212	C₂²×C₄₇	—	8	4	no	—
213	C₂²×C₄₇	#388	1	2	yes	—
214	C₂²×C₄₇	#388	1	2	yes	—
215	C₂²×C₄₇	#444	1	4	yes	—
216	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
219	C₄×C₄₇	—	4	4	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	#388	1	2	yes	—
222	C₄×C₄₇	#388	1	2	yes	—
223	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
224	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
226	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
227	Dic₄₇	—	4	4	no	—
228	C₂×#424	—	47	1	no	—
229	C₂²×#104	D₄₇	1	1	yes	characteristic
230	C₂×#416	—	47	1	no	—
231	C₂×#408	—	47	1	no	—
232	C₂²×#97	—	47	1	no	—
233	#1938	—	47	8	no	—
234	C₂×#341	—	47	1	no	—
235	C₂×#339	—	47	1	no	—
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	2	no	—
239	C₂×C₄₇	—	8	2	no	—
240	C₂×C₄₇	#1938	1	4	yes	complemented
241	C₂×C₄₇	C₂×#388	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#444	1	2	yes	—
243	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
244	C₂²×M₁₆	—	47	1	no	—
245	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
246	C₂³×C₈	—	47	1	no	—
247	C₂³×C₈	—	47	1	no	—
248	C₂×#117	—	47	1	no	—
249	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
250	#424	—	47	4	no	—
251	#424	—	94	2	no	—
252	C₂×C₄⋊C₈	—	94	2	no	—
253	C₂×#104	—	2	4	no	—
254	C₂×#104	C₂×D₄₇	1	4	yes	—
255	#416	—	47	4	no	—
256	#416	—	47	4	no	—
257	C₂×#103	—	47	2	no	—
258	C₂×#102	—	47	2	no	—
259	#408	—	47	4	no	—
260	#408	—	94	2	no	—
261	C₂×C₂²⋊C₈	—	94	2	no	—
262	C₂×#97	—	47	4	no	—
263	C₂×#97	—	94	4	no	—
264	#341	—	47	4	no	—
265	#339	—	47	4	no	—
266	C₄₇	C₂×#1938	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	C₄×D₄₇	1	2	yes	—
274	C₂×#41	C₂²×D₄₇	1	2	yes	—
275	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	47	2	no	—
285	C₂×M₁₆	—	94	1	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	47	2	no	—
291	C₂²×C₈	—	47	2	no	—
292	C₂²×C₈	—	47	2	no	—
293	C₂²×C₈	—	47	2	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²×C₈	—	47	2	no	—
296	C₂²×C₈	—	94	2	no	—
297	C₂²×C₈	—	94	2	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	—	94	2	no	—
300	C₂²×C₈	—	94	1	no	—
301	#117	—	47	2	no	—
302	#117	—	47	2	no	—
303	#117	—	94	1	no	—
304	#117	—	94	1	no	—
305	C₂×C₄⋊C₄	—	47	2	no	—
306	C₂×C₂²⋊C₄	—	94	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	94	1	no	—
310	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
311	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
312	C₄⋊C₈	—	94	8	no	—
313	#104	—	2	8	no	—
314	#103	—	47	8	no	—
315	#102	—	47	8	no	—
316	C₂²⋊C₈	—	94	8	no	—
317	#97	—	94	8	no	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	#10625352	1	1	yes	characteristic
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	4	2	no	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	#41	—	4	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	94	2	no	—
351	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	#10625350	1	2	yes	—
354	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
356	C₂²×C₄	#10625352	1	2	yes	—
357	C₂²×C₄	#10625352	1	2	yes	—
358	C₂²×C₄	#10625352	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
360	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	4	2	no	—
364	M₁₆	—	94	2	no	—
365	M₁₆	—	94	2	no	—
366	M₁₆	—	188	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	47	4	no	—
370	C₂×C₈	—	47	4	no	—
371	C₂×C₈	—	94	4	no	—
372	C₂×C₈	—	94	4	no	—
373	C₂×C₈	—	94	4	no	—
374	C₂×C₈	—	94	4	no	—
375	C₂×C₈	—	94	2	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	188	2	no	—
381	C₄⋊C₄	—	47	4	no	—
382	C₄⋊C₄	—	94	2	no	—
383	C₂²⋊C₄	—	94	2	no	—
384	C₂²⋊C₄	—	94	2	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	94	2	no	—
388	C₄²	—	94	2	no	—
389	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	2	no	—
394	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
395	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
396	C₂³	#13094005	1	2	yes	—
397	C₂³	#13094017	1	2	yes	—
398	C₂³	C₂×#10625352	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	4	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	94	4	no	—
417	C₂×C₄	—	188	4	no	—
418	C₂×C₄	#13093980	1	2	yes	—
419	C₂×C₄	#13093980	1	2	yes	—
420	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
421	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
423	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
424	C₂×C₄	#13093995	1	2	yes	—
425	C₂×C₄	#13093995	1	2	yes	—
426	C₂×C₄	#13094005	1	2	yes	—
427	C₂×C₄	#13094010	1	2	yes	—
428	C₂×C₄	#13094010	1	2	yes	—
429	C₂×C₄	#13094017	1	2	yes	—
430	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
434	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
435	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	94	4	no	—
438	C₈	—	94	4	no	—
439	C₈	—	188	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	4	no	—
447	C₂²	#15689011	1	2	yes	—
448	C₂²	#15689011	1	2	yes	—
449	C₂²	#15689242	1	4	yes	—
450	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
451	C₂²	C₂×#13094005	1	1	yes	characteristic
452	C₂²	C₂×#13094017	1	1	yes	characteristic
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	188	4	no	—
456	C₄	#15689011	1	2	yes	—
457	C₄	#15689011	1	2	yes	—
458	C₄	C₂×#13093980	1	1	yes	characteristic
459	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
460	C₄	C₂×#13093995	1	1	yes	characteristic
461	C₄	C₂×#13094010	1	1	yes	characteristic
462	C₂	—	2	1	no	—
463	C₂	—	2	2	no	—
464	C₂	—	2	1	no	—
465	C₂	—	8	2	no	—
466	C₂	#20244096	1	4	yes	direct product factor
467	C₂	C₂×#15689011	1	1	yes	characteristic
468	C₂	C₂×#15689242	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#104×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#104	D₄₇
hypocenter	C₄₇	C₂×#1938
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#15689151	C₂	semidirect
4. C₂²×#13093935	C₂	semidirect
5. #20244096	C₂	direct (N × H)
6. C₂×#15688887	C₂	semidirect
7. C₂×#15688883	C₂	semidirect
14. #15689151	C₂²	semidirect
16. #15689119	C₄	semidirect
18. C₂×#13093948	C₄	semidirect
19. C₂×#13093945	C₄	semidirect
24. C₂×#13093935	C₂²	semidirect
25. #15688887	C₂²	semidirect
26. #15688883	C₂²	semidirect
55. #13093948	C₂×C₄	semidirect
56. #13093945	C₂×C₄	semidirect
240. C₂×C₄₇	#1938	semidirect
266. C₄₇	C₂×#1938	semidirect
466. C₂	#20244096	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689151	2
C₂×#15689119	2
C₂×#15689090	2
C₂²×#13093935	2
#20244096	2
C₂×#15688887	2
C₂×#15688883	2
C₂²×#104×C₄₇	2
C₂×#1938	47

Subgroups — C2×#20244096 #26219017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244096 #26219017